RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-11-28_10:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 15.74 12.1700 0.210264 2 to 25 15.65 23.3050 0.860418 3 to 26 15.56 15.9788 0.474665 4 to 27 15.72 12.8211 0.251920 5 to 28 15.78 13.1812 0.276028 6 to 29 15.52 23.7045 0.872312 7 to 30 15.86 11.0079 0.143848 8 to 31 15.86 25.7147 0.920182 9 to 32 15.76 11.6151 0.177137 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.534598 Tough bday spacings test for dh-ranFile-2015-11-28_10:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 7 38 71 101 96 88 52 25 13 6 3 (O-E)^2/E 0.5 0.1 0.1 0.1 0.0 1.2 0.0 0.8 0.2 0.1 0.3 Birthday Spacings: Sum(O-E)^2/E= 3.354, p= 0.028 RESULTS OF GCD FOR dh-ranFile-2015-11-28_10:31 Euclid's algorithm: p-value, steps to gcd: 0.008556 p-value, dist. of gcd's: 0.164998 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-11-28_10:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.691 0.393 0.709 0.579 0.606 0.059 0.923 0.795 Bits 8 to 15---> 0.666 0.233 0.981 0.736 0.362 1.000 0.475 0.436 Bits 16 to 23---> 0.024 0.372 0.930 0.509 0.730 0.699 0.938 0.078 Bits 24 to 31---> 0.549 0.779 0.782 0.445 0.585 0.383 0.383 0.239 KS test for the above 32 p values: 0.774 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-11-28_10:31, p-values for 5 runs: 0.6253, 0.0819, 0.9806, 0.7733, 0.9926 Rank test for binary matrices (31x31) for dh-ranFile-2015-11-28_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 221 211.4 0.434 0.434 r= 29 5145 5134.0 0.024 0.458 r= 30 23086 23103.0 0.013 0.470 r= 31 11548 11551.5 0.001 0.471 chi-square = 0.471 with df = 3; p-value = 0.075 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-11-28_10:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 199 211.4 0.729 0.729 r= 30 5128 5134.0 0.007 0.736 r= 31 23122 23103.0 0.016 0.752 r= 32 11551 11551.5 0.000 0.752 chi-square = 0.752 with df = 3; p-value = 0.139 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-11-28_10:31 b-rank test for bits 1 to 8, p=0.05194 b-rank test for bits 2 to 9, p=0.07854 b-rank test for bits 3 to 10, p=0.50575 b-rank test for bits 4 to 11, p=0.16373 b-rank test for bits 5 to 12, p=0.01814 b-rank test for bits 6 to 13, p=0.03241 b-rank test for bits 7 to 14, p=0.40376 b-rank test for bits 8 to 15, p=0.98426 b-rank test for bits 9 to 16, p=0.97544 b-rank test for bits 10 to 17, p=0.66340 b-rank test for bits 11 to 18, p=0.43748 b-rank test for bits 12 to 19, p=0.35616 b-rank test for bits 13 to 20, p=0.82431 b-rank test for bits 14 to 21, p=0.39608 b-rank test for bits 15 to 22, p=0.22184 b-rank test for bits 16 to 23, p=0.35652 b-rank test for bits 17 to 24, p=0.92252 b-rank test for bits 18 to 25, p=0.13703 b-rank test for bits 19 to 26, p=0.75023 b-rank test for bits 20 to 27, p=0.65425 b-rank test for bits 21 to 28, p=0.38779 b-rank test for bits 22 to 29, p=0.05684 b-rank test for bits 23 to 30, p=0.87775 b-rank test for bits 24 to 31, p=0.30528 b-rank test for bits 25 to 32, p=0.28514 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.298729 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-11-28_10:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141136 -1.81 0.035393 2 141603 -0.72 0.237081 3 142345 1.02 0.845642 4 142775 2.02 0.978442 5 141548 -0.84 0.199271 6 141951 0.10 0.538780 7 142395 1.13 0.871759 8 142016 0.25 0.598408 9 142094 0.43 0.666937 10 142812 2.11 0.982530 11 141292 -1.44 0.074600 12 142057 0.35 0.634962 13 141662 -0.58 0.281675 14 141641 -0.63 0.265350 15 141782 -0.30 0.383042 16 142939 2.41 0.991931 17 141261 -1.51 0.064913 18 142381 1.10 0.864776 19 141737 -0.40 0.343607 20 141079 -1.94 0.026188 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-11-28_10:31 Bits used No. missing words z-score p-value 23 to 32 142169 0.8954 0.814717 22 to 31 142049 0.4816 0.684962 21 to 30 142080 0.5885 0.721907 20 to 29 141716 -0.6667 0.252496 19 to 28 141931 0.0747 0.529783 18 to 27 142097 0.6471 0.741229 17 to 26 141759 -0.5184 0.302097 16 to 25 141968 0.2023 0.580163 15 to 24 141634 -0.9494 0.171205 14 to 23 141899 -0.0356 0.485792 13 to 22 141464 -1.5356 0.062316 12 to 21 142111 0.6954 0.756602 11 to 20 141573 -1.1598 0.123074 10 to 19 141495 -1.4287 0.076542 9 to 18 141367 -1.8701 0.030735 8 to 17 141900 -0.0322 0.487167 7 to 16 141959 0.1713 0.567997 6 to 15 142000 0.3127 0.622729 5 to 14 141970 0.2092 0.582857 4 to 13 142024 0.3954 0.653731 3 to 12 141692 -0.7494 0.226804 2 to 11 141902 -0.0253 0.489918 1 to 10 141981 0.2471 0.597599 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-11-28_10:31 Bits used No. missing words z-score p-value 28 to 32 141745 -0.5571 0.288746 27 to 31 141875 -0.1164 0.453679 26 to 30 142477 1.9243 0.972842 25 to 29 141901 -0.0282 0.488737 24 to 28 142478 1.9277 0.973053 23 to 27 141955 0.1548 0.561516 22 to 26 141259 -2.2045 0.013744 21 to 25 142363 1.5379 0.937959 20 to 24 141909 -0.0011 0.499554 19 to 23 141921 0.0396 0.515778 18 to 22 141435 -1.6079 0.053929 17 to 21 141884 -0.0859 0.465787 16 to 20 141500 -1.3876 0.082636 15 to 19 141729 -0.6113 0.270504 14 to 18 142010 0.3413 0.633544 13 to 17 141904 -0.0181 0.492792 12 to 16 141836 -0.2486 0.401844 11 to 15 141838 -0.2418 0.404469 10 to 14 141542 -1.2452 0.106532 9 to 13 141996 0.2938 0.615543 8 to 12 141997 0.2972 0.616838 7 to 11 142259 1.1853 0.882055 6 to 10 141833 -0.2587 0.397916 5 to 9 141911 0.0057 0.502258 4 to 8 142298 1.3175 0.906169 3 to 7 141859 -0.1706 0.432265 2 to 6 141762 -0.4994 0.308741 1 to 5 142040 0.4429 0.671099 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-11-28_10:31 Bits used No. missing words z-score p-value 31 to 32 141701 -0.6145 0.269428 30 to 31 141452 -1.3491 0.088660 29 to 30 142286 1.1111 0.866742 28 to 29 141577 -0.9803 0.163463 27 to 28 141651 -0.7620 0.223019 26 to 27 141829 -0.2370 0.406343 25 to 26 142240 0.9754 0.835326 24 to 25 142270 1.0639 0.856318 23 to 24 141713 -0.5791 0.281246 22 to 23 141392 -1.5260 0.063499 21 to 22 142111 0.5949 0.724044 20 to 21 142032 0.3619 0.641271 19 to 20 142272 1.0698 0.857651 18 to 19 142317 1.2026 0.885428 17 to 18 142655 2.1996 0.986083 16 to 17 141938 0.0846 0.533699 15 to 16 141558 -1.0364 0.150014 14 to 15 141806 -0.3048 0.380256 13 to 14 141884 -0.0747 0.470219 12 to 13 142112 0.5978 0.725029 11 to 12 141901 -0.0246 0.490198 10 to 11 142000 0.2675 0.605444 9 to 10 142447 1.5860 0.943636 8 to 9 142337 1.2616 0.896447 7 to 8 141457 -1.3343 0.091052 6 to 7 141928 0.0551 0.521960 5 to 6 142366 1.3471 0.911027 4 to 5 142062 0.4504 0.673772 3 to 4 141754 -0.4582 0.323404 2 to 3 141781 -0.3786 0.352509 1 to 2 141662 -0.7296 0.232821 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-11-28_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2411.56 -1.251 0.105526 Test results for specific bytes for dh-ranFile-2015-11-28_10:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2418.39 -1.154 0.124225 2 to 9 2409.02 -1.287 0.099102 3 to 10 2511.86 0.168 0.566602 4 to 11 2478.35 -0.306 0.379733 5 to 12 2458.09 -0.593 0.276711 6 to 13 2421.89 -1.105 0.134655 7 to 14 2433.23 -0.944 0.172509 8 to 15 2591.74 1.297 0.902753 9 to 16 2536.38 0.515 0.696566 10 to 17 2507.35 0.104 0.541405 11 to 18 2498.22 -0.025 0.489945 12 to 19 2499.94 -0.001 0.499641 13 to 20 2470.33 -0.420 0.337408 14 to 21 2563.19 0.894 0.814239 15 to 22 2518.91 0.267 0.605425 16 to 23 2451.71 -0.683 0.247347 17 to 24 2368.67 -1.857 0.031636 18 to 25 2489.47 -0.149 0.440831 19 to 26 2398.49 -1.436 0.075571 20 to 27 2595.38 1.349 0.911308 21 to 28 2591.81 1.298 0.902913 22 to 29 2512.14 0.172 0.568144 23 to 30 2468.79 -0.441 0.329481 24 to 31 2497.33 -0.038 0.484962 25 to 32 2506.78 0.096 0.538188 CDPARK for dh-ranFile-2015-11-28_10:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3543 0.9132 0.819442 3522 -0.0457 0.481790 3502 -0.9589 0.168804 3524 0.0457 0.518210 3537 0.6393 0.738676 3532 0.4110 0.659449 3541 0.8219 0.794438 3516 -0.3196 0.374623 3540 0.7763 0.781201 3496 -1.2329 0.108811 Square side=100, avg. no. parked=3525.30 sample std.=15.68 p-value of the KSTEST for those 10 p-values: 0.695881 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-11-28_10:31 0.1930,0.4577,0.2063,0.7716,0.8256,0.0371,0.7628,0.7833,0.0480,0.6036, The KS test for those 10 p-values: 0.639070 The 3DSPHERES test for dh-ranFile-2015-11-28_10:31 sample no r^3 equiv. uni. 1 15.264 0.398789 2 8.060 0.235603 3 6.184 0.186278 4 20.827 0.500538 5 46.046 0.784516 6 79.804 0.930062 7 9.459 0.270430 8 5.902 0.178604 9 15.922 0.411817 10 66.679 0.891676 11 0.640 0.021118 12 19.537 0.478597 13 17.604 0.443897 14 3.614 0.113499 15 55.166 0.841003 16 18.176 0.454399 17 5.696 0.172938 18 0.478 0.015814 19 8.252 0.240468 20 30.178 0.634303 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.256363 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-11-28_10:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.8 -0.7 -0.1 -0.3 -1.3 2.0 0.1 -1.7 0.7 -0.1 -1.0 -0.8 1.4 0.2 -0.2 -0.3 1.1 1.1 -0.4 0.4 1.2 -1.9 -1.2 -0.1 0.3 1.1 -0.0 -0.9 -3.2 1.2 0.7 1.0 0.3 -1.7 -0.6 2.6 -1.4 -0.7 -1.6 -0.1 0.9 -1.0 0.8 Chi-square with 42 degrees of freedom:55.810746 z-score=1.506876, p-value=0.924867 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-11-28_10:31 Test no p-value 1 0.158068 2 0.809809 3 0.013711 4 0.349204 5 0.290706 6 0.261125 7 0.087632 8 0.002824 9 0.029011 10 0.014448 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.000193 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-11-28_10:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66891 0.75 66808 0.30 3 25000.00 24678 4.15 24865 0.73 4 6666.67 6796 2.51 6701 0.18 5 1388.89 1356 0.78 1364 0.45 6 238.10 233 0.11 229 0.35 7 34.72 38 0.31 26 2.19 8 4.96 7 0.84 6 0.22 p=0.85009 p=0.37822 Number of rngs required: 687474, p-value: 0.141 RESULTS OF CRAPS TEST for dh-ranFile-2015-11-28_10:31 No. of wins: Observed Expected 98758 98585.9 z-score= 0.770, pvalue=0.77933 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66810 66666.7 0.308 0.308 2 37608 37654.3 0.057 0.365 3 26994 26954.7 0.057 0.422 4 19437 19313.5 0.790 1.213 5 13702 13851.4 1.612 2.824 6 9994 9943.5 0.256 3.080 7 7203 7145.0 0.470 3.551 8 4957 5139.1 6.451 10.001 9 3659 3699.9 0.451 10.453 10 2680 2666.3 0.070 10.523 11 1841 1923.3 3.524 14.047 12 1385 1388.7 0.010 14.057 13 1035 1003.7 0.975 15.033 14 728 726.1 0.005 15.037 15 544 525.8 0.627 15.665 16 339 381.2 4.661 20.326 17 292 276.5 0.864 21.190 18 239 200.8 7.255 28.445 19 152 146.0 0.248 28.693 20 105 106.2 0.014 28.707 21 296 287.1 0.275 28.982 Chisq= 28.98 for 20 degrees of freedom, p= 0.91189 SUMMARY of craptest p-value for no. of wins: 0.779325 p-value for throws/game: 0.911885 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-11-28_10:31 No. of wins: Observed Expected 98240 98585.9 z-score=-1.547, pvalue=0.06095 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66220 66666.7 2.993 2.993 2 37747 37654.3 0.228 3.221 3 27014 26954.7 0.130 3.351 4 19489 19313.5 1.595 4.947 5 13993 13851.4 1.447 6.394 6 9924 9943.5 0.038 6.432 7 7121 7145.0 0.081 6.513 8 5118 5139.1 0.086 6.599 9 3594 3699.9 3.029 9.628 10 2681 2666.3 0.081 9.709 11 1971 1923.3 1.182 10.891 12 1363 1388.7 0.477 11.368 13 1025 1003.7 0.451 11.820 14 739 726.1 0.228 12.047 15 543 525.8 0.560 12.607 16 384 381.2 0.021 12.629 17 305 276.5 2.929 15.558 18 203 200.8 0.023 15.581 19 168 146.0 3.320 18.901 20 106 106.2 0.000 18.902 21 292 287.1 0.083 18.985 Chisq= 18.99 for 20 degrees of freedom, p= 0.47720 SUMMARY of craptest p-value for no. of wins: 0.060946 p-value for throws/game: 0.477201 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0002,0.0028,0.0086,0.0137,0.0137,0.0144,0.0158,0.0181,0.0211,0.0244, 0.0262,0.0282,0.0290,0.0307,0.0316,0.0324,0.0354,0.0371,0.0480,0.0519, 0.0539,0.0568,0.0591,0.0609,0.0623,0.0635,0.0649,0.0746,0.0749,0.0756, 0.0765,0.0782,0.0785,0.0819,0.0826,0.0876,0.0887,0.0911,0.0991,0.1055, 0.1065,0.1088,0.1135,0.1231,0.1242,0.1347,0.1370,0.1391,0.1406,0.1438, 0.1500,0.1581,0.1635,0.1637,0.1650,0.1688,0.1712,0.1725,0.1729,0.1771, 0.1786,0.1863,0.1930,0.1993,0.2063,0.2103,0.2218,0.2230,0.2268,0.2326, 0.2328,0.2356,0.2371,0.2391,0.2405,0.2473,0.2519,0.2525,0.2564,0.2611, 0.2653,0.2694,0.2704,0.2705,0.2760,0.2767,0.2812,0.2817,0.2851,0.2887, 0.2907,0.2987,0.3021,0.3053,0.3087,0.3234,0.3295,0.3374,0.3436,0.3492, 0.3525,0.3562,0.3565,0.3617,0.3722,0.3746,0.3782,0.3797,0.3803,0.3829, 0.3830,0.3833,0.3878,0.3932,0.3961,0.3979,0.3988,0.4018,0.4038,0.4045, 0.4063,0.4118,0.4323,0.4359,0.4375,0.4408,0.4439,0.4447,0.4537,0.4544, 0.4577,0.4658,0.4702,0.4747,0.4750,0.4772,0.4786,0.4818,0.4850,0.4858, 0.4872,0.4887,0.4899,0.4899,0.4902,0.4928,0.4996,0.4996,0.5005,0.5023, 0.5058,0.5091,0.5158,0.5182,0.5220,0.5298,0.5337,0.5346,0.5382,0.5388, 0.5414,0.5494,0.5615,0.5666,0.5680,0.5681,0.5793,0.5802,0.5829,0.5849, 0.5976,0.5984,0.6036,0.6054,0.6054,0.6056,0.6155,0.6168,0.6227,0.6253, 0.6335,0.6343,0.6350,0.6391,0.6413,0.6537,0.6543,0.6594,0.6634,0.6656, 0.6669,0.6711,0.6738,0.6850,0.6915,0.6959,0.6966,0.6989,0.7094,0.7219, 0.7240,0.7250,0.7300,0.7356,0.7387,0.7412,0.7502,0.7566,0.7628,0.7716, 0.7733,0.7742,0.7786,0.7793,0.7812,0.7817,0.7833,0.7845,0.7944,0.7946, 0.8098,0.8142,0.8147,0.8194,0.8243,0.8256,0.8353,0.8410,0.8456,0.8501, 0.8563,0.8577,0.8604,0.8648,0.8667,0.8718,0.8723,0.8777,0.8821,0.8854, 0.8917,0.8964,0.9028,0.9029,0.9062,0.9110,0.9113,0.9119,0.9202,0.9225, 0.9229,0.9249,0.9301,0.9303,0.9376,0.9380,0.9436,0.9728,0.9731,0.9754, 0.9784,0.9806,0.9812,0.9825,0.9843,0.9861,0.9919,0.9926,1.0000, Overall p-value after applying KStest on 269 p-values = 0.140280 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.